Covert JPG Logo to High Resolution PSD Photoshop Logo

We have a JPG copy of logo. The logo displays on places like a website, but when you blow it up / enlarge it to a much larger image, the logo's 'curve' starts showing jagged edges.

We want the curve on the logo to show smooth curve line when enlarged.

Existing JPG Logo is attached which is also available at [url removed, login to view]

TASK TO DO

- Make a New Photoshop Logo PSD File (Very High Quality - Very High Resolution) (Highest possible resolution - so that I can make a banner that may be 5 feet wide by 3 feet high, and the logo will look smooth and crisp)

- The new logo should look 'near' identical to existing logo (similar text font - similar colors, similar spacing between characters)